Two byte pointers away from the "Slot" pointer under Camp is appearantly a pointer for the skin of the character. This only seems to work on Lazarel and Teresa though. Changing the skin and party slot for any other character to one that's not theirs, will make them not appear once you enter a new area, and the game will eventually crash.
I noticed that when you change to a different character, like one of the DLC characters from Heroes 1, only some of the skills Lazarel/Teresa had equipped appear when you bring up the skill ring, so that's a side effect I noticed.
I'm mostly posting this updated table to see if DrummerIX might be able to look more into how this works and if there's other skin pointers that affect this, being it would be nice to be able to more consistantly use DLC characters outside of the special dungeons. :V
Proof below [Teresa [Sage] as Nera in the first major Wild Zone]: